Variable-Precision Approximate Floating-Point Multiplier for Efficient Deep Learning Computation
Bibliographic record
Abstract
In this brief, a variable-precision approximate floating-point multiplier is proposed for energy efficient deep learning computation. The proposed architecture supports approximate multiplication with BFloat16 format. As the input and output activations of deep learning models usually follow normal distribution, inspired by the posit format, for numbers with different values, different precisions can be applied to represent them. In the proposed architecture, posit encoding is used to change the level of approximation, and the precision of the computation is controlled by the value of product exponent. For large exponent, smaller precision multiplication is applied to mantissa and for small exponent, higher precision computation is applied. Truncation is used as approximate method in the proposed design while the number of bit positions to be truncated is controlled by the values of the product exponent. The proposed design can achieve 19% area reduction and 42% power reduction compared to the normal BFloat16 multiplier. When applying the proposed multiplier in deep learning computation, almost the same accuracy as that of normal BFloat16 multiplier can be achieved.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".